1.

Prove that a pipe of length 2L open at both ends has the same fundamental frequency as a pipe of length L closed at one end.

Answer»

Let LO and LC be the lengths of a pipe open at both ends and a pipe closed at one end, respectively. Let nO and nC be their corresponding fundamental frequencies. Then, ignoring the end corrections,

n\(\frac v{2L_O}\) and nC = \(\frac v{4L_O}\)

where v is the speed of the sound in air.

Given that LC = L and LO = 2L,

nO = \(\frac v{4L}\)and nC = \(\frac v{4L}\)

∴ nO = nC



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